AbstractIt has been observed in literature that the stability of tyrosinase‐mimicked μ‐η²:η²‐peroxo‐dicopper(II) (P) can be perturbed in presence of counter‐anions (CAs) such as PhCO₂⁻, CF₃SO₃⁻, TsO⁻ and SbF₆⁻. In this work, we unravel computational indicators using density functional theory to screen and study the stability of P in experimentally‐reported cases. These indicators are Gibbs energies, geometrical parameters such as distances and angles, independent gradient model based on Hirshfeld partition (IGMH) generated data, orbitals’ overlap, and distortion‐interaction (DI) energies. Our DFT computed Gibbs energies indicate that P is stable in case of PhCO₂⁻ and TsO⁻. CF₃SO₃⁻ allows P and its isoelectronic species bis‐μ‐oxo‐dicopper (O) to coexist. SbF₆⁻ shows that O is in excess. Our indicators reveal that the stability of P in case of PhCO₂⁻ and TsO⁻ is due to the better placing of P and its CA, thus leading to better interactions and overlap of orbitals. Other indicator displays that the plane of Cu₂O₂ core in P is more bend in PhCO₂⁻ and TsO⁻ cases as compared to the plane in the other two cases. In addition, the IGMH‐based indicator displays higher values in the case of PhCO₂⁻ and TsO⁻ than the other CAs.